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"successively higher" is correct and usable in written English.
Adjectives like "successively" are used to describe how something changes or moves over time, and can be used in a variety of contexts. For example, "As the graph moved from left to right, the green line rose successively higher."
Exact(60)
Successive periods down the table correspond to successively higher values of n for the valence shell.
The first integer is a radial quantum number taking successive values 1, 2, 3, etc., for successively higher energy values of an orbital of given l and j.
This process can be continued indefinitely to build multigrades of successively higher orders.
He has been fasting to lower his body weight and practicing landing properly from successively higher jumps.
From there, Athenagoras' career in the church progressed through successively higher offices.
In cross-section, the island looks like a staircase, composed of successively higher cliffs and terraces as one moves inland.
Government officials simulated a number of economic scenarios, involving successively higher rates of loan defaults, to see if the banks had enough capital to withstand losses.
points are lost with each successively higher level of exposure -- the city has an obligation, they say, to take action where it can.
William J. Casey, whom Reagan had named director of central intelligence, appointed Mr. George to successively higher positions.
At successively higher elevations are found subalpine meadow and alpine tundra plant communities that in summer abound in wildflowers.
As evolution progressed, cells of successively higher levels of complexity must have arisen, and it was absolutely essential that they had the ability to make likenesses of themselves.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com